ConceptTrigonometric Identities

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#### Question

If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.

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#### Similar questions

Prove the following identities:

`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`

`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`

`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`

Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec^{2} θ = 1 + tan^{2} θ.

Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`

Evaluate

`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^@73^@)`